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Applications of line objects in robotics. (English) Zbl 1046.70004
Summary: The Lie algebra of Lie group of Euclidean motions in \(E_3\) is represented as the vector space \(A_6\) of couples of vectors in \(E_3\). We describe all subalgebras and all 3-dimensional subspaces of \(A_6\) which are orthogonal to themselves according to the Klein form, and give their kinematic interpretations. Vector fields in \(E_3\) determined by elements of \(A_6\) and their kinematic and dynamic interpretations are investigated.

MSC:
70B15 Kinematics of mechanisms and robots
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
22E70 Applications of Lie groups to the sciences; explicit representations
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